Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}-2x+6y &= -6 \\ -x+8y &= 2\end{align*}$
Explanation: Begin by moving the $x$ -term in the second equation to the right side of the equation. $8y = x+2$ Divide both sides by $8$ to isolate $y$ $y = {\dfrac{1}{8}x + \dfrac{1}{4}}$ Substitute this expression for $y$ in the first equation. $-2x+6({\dfrac{1}{8}x + \dfrac{1}{4}}) = -6$ $-2x + \dfrac{3}{4}x + \dfrac{3}{2} = -6$ Simplify by combining terms, then solve for $x$ $-\dfrac{5}{4}x + \dfrac{3}{2} = -6$ $-\dfrac{5}{4}x = -\dfrac{15}{2}$ $x = 6$ Substitute $6$ for $x$ back into the top equation. $-2( 6)+6y = -6$ $-12+6y = -6$ $6y = 6$ $y = 1$ The solution is $\enspace x = 6, \enspace y = 1$.